Orbital Mechanics

On By Matt FraserIn Science and Technology3 Comments

In my previous post I referred to some difficulties encountered with the mechanics of Aniara‘s orbit with respect to the ring space station the crew is investigating. I mentioned how they could not simply park the ship 100 km away at the same altitude, paralleling the station’s orbit around the planet, without risking eventually colliding with the station.

Why not?

It has to do with a basic principle of orbiting a planetary body, whether it’s Earth or any other planet (such as Kepler 62f, for example). Any satellite or object in orbit describes an ellipse or circle as it moves through its orbit, and the center of that circle is the center of the planet itself. It’s not some point 100 km away from the planet’s center, it is exactly the planet’s center.

This means that any orbit that isn’t exactly above the equator must be at a particular angle of inclination away from the equator:

orbital_inclination
image credit: Robert Simmon / NASA

Granted, at only 100 km distance, the inclination would not be this extreme. Given that the orbit is at Kepler 62f’s geostationary altitude of 41,100 km, and therefore has a radius of 50,030 km (I’m assuming Kepler 62f’s diameter is 17,860 km, so yes, a bit larger than Earth), that gives the angle of inclination at 0.72°.

Perhaps an even more clear illustration of this effect, with plenty of technical astrodynamics terms thrown in for good measure:

Orbit1
image credit: user:Lasunncty / Wikipedia

So you see, that slightly north-inclined orbit would not parallel the equatorial orbit (which the station is following), nor even remain north-inclined for long. Instead, any such satellite (or ship) would spend half its orbit north of the equator, and half its orbit south of the equator (assuming the orbit is circular). If the orbit is at a different altitude, then this doesn’t represent any particular issue, but if it’s at the same altitude…

Yeah, that’s right. Since the station is a ring completely encircling the planet, Aniara would have made exactly half of an orbit before smashing into it. Not good for our crew, not good at all.

A far better option, then, is to choose a different altitude. So, instead, Aniara parks 100 km above the station, rather than beside it. This way, Aniara can maintain the same equatorial orbit and just hover there, right?

Well, almost. Not quite perfectly, as it turns out.

You see, every orbit has precisely one speed at which that orbit can be maintained. This can be an even harder concept to fully grasp than inclined angles circling around the center of the planet, but the best way to think of it is that the satellite is falling toward the planet at all times. It is called free fall, after all. The planet’s gravity is constantly pulling the satellite down. But, because the satellite has a tangential velocity vector…

Wait, what? Oh, hey, it’s been years since high school trigonometry, are you really going to lay that on me?

Ok, ok, I’ll back off just a little bit. So, the satellite is falling, but it’s not falling straight down, it’s falling at an angle, or rather in a high arc. And, it’s falling really, really fast. So fast, in fact, that it’s arc keeps on missing the planet and it falls past it. Except, as it falls past it, the planet’s gravity keeps trying to pull it down, so the arc keeps bending toward the planet, but never quite intersects the planet. The satellite falls past, and down, and past, and down, and so on, in a theoretically never-ending circle (or ellipse, more accurately).

The closer to the planet the satellite is, the more effect the gravity has on it, so it falls faster. But, because it falls faster, the arc always remains above the planet’s surface. In contrast, the farther from the planet the satellite is, the slower it moves.

Now here’s where things get really weird for most folks. Let’s say your spaceship is orbiting the planet, nice and stable like. Everything is great, yet you decide you really want to bring the ship down to a lower orbit. As if, for instance, you were descending to park closer to an alien space station you had just spent a few days observing from higher altitude.

You could just angle your ship nose down and fire the engines, powering your way down, but this would have the undesirable effect of changing the shape of your orbit. Where before perhaps you had been in a nicely circular orbit, now you would be in a much more highly eccentric elliptical orbit, which wouldn’t do at all if your intent was to park over the station with its own circular orbit.

Ok, so you can’t just power your way down there. Instead, your fire your engines in retrograde, meaning in the forward direction, to push back on your ship’s velocity vector. This has the desired effect of causing your ship to fall closer to the planet indeed, and nicely reduces the altitude of your orbit, but perhaps counter-intuitively it also causes your ship to speed up.

That’s right. Fire your engines in reverse, and you go faster. You descend, but you go faster.

dawn_orbits-20150527
image credit: NASA

By the same token, if you fire your engines prograde, meaning to push your ship forward, you will ascend to a higher orbit and go slower.

Well, that is, unless you fire them with enough thrust to overcome the planet’s escape velocity, thus leaving its orbit entirely, but that’s a different maneuver.

So what does this mean for Aniara, after descending, but parking 100 km higher than the alien station? She isn’t at the same altitude, so we know that she cannot orbit at the same speed. Indeed, she must be going slower. How much slower?

Orbital velocity for a circular orbit is defined by the equation √(GM/r), where G is the universal gravitational constant, M is the mass of the planet, and r is the radius of the orbit. There can be a lot of unknowns here, and often it’s easier to think of GM together (sometimes written as µ) as a given planet’s standard gravitational parameter. Kepler 62f’s exact gravitational parameter isn’t of supreme importance here, but rather from this we can determine that if the orbital velocity at 41,100 km altitude (50,030 km radius) is, say 3,000 m/s (which would be a reasonable velocity for that altitude for a planet of slightly higher mass than Earth, so let’s just go with that), then orbital velocity for an altitude 100 km higher would be 2,997 m/s.

So, Aniara drifts “backwards” relative to the station at a rate of 3 m/s, or roughly 10.8 km/h.

Astute readers will recall that this station has twelve tether counterweights (in various states of disrepair) extending upward for a considerable distance, certainly quite a lot higher than 100 km. How long before Aniara drifts backwards into one? Or more accurately, until one of them catches up to Aniara and knocks her out of her orbit (or worse)? Assuming the twelve tethers are equidistant around the globe, at this altitude that makes them more than 26,000 km apart from each other. At not quite 11 km/hr, Aniara has over 100 “Earth” days before this becomes a problem.

Depending on what happens, this could become a problem; possible plot point? Who knows? You’ll just have to wait and see. But it’s a reasonable assumption that the crew does not expect to maintain this same orbit for that long.

So why 41,100 km altitude for the station? What makes this altitude geostationary? Of course, I recognize that the word geostationary is inaccurate, as geo refers to our own planet Earth, and this isn’t Earth we’re orbiting now. But, kepler62fstationary just doesn’t sound right. Ok, semantics aside, remember how orbital velocity is a direct result of orbital altitude? For any given altitude, there is a defined orbital speed, and for any given speed, there is a defined orbital altitude. And it so happens that there is an altitude at which a satellite’s orbital speed is precisely matched to the angular momentum (I think I’m using the right term there — remember, long years since high school trigonometry?) so that the satellite is apparently motionless above the planet, or stationary. Around Earth, this altitude is approximately 36,000 km, but because Kepler 62f is a slightly bigger planet, the “geo”stationary altitude is slightly higher. I admit it, I just picked a number that seemed reasonable and went with 41,100 km. And yes, about 3,000 m/s would be an appropriate speed at this altitude for the presumed mass of this planet.

One final note about geostationary orbits: they are only possible with an inclination of 0°, or directly above the equator, and with a near-zero eccentricity, meaning practically circular orbit. Any other inclination, and the satellite will still revolve evenly with the planet’s surface, but it will appear to migrate north and south in a figure-8 pattern. This would be a geosynchronous orbit, but not geostationary.

One final, final note about ring stations with multiple tethers reaching all the way to the planet’s surface: I’m fairly certain that any satellites orbiting at a lower altitude would eventually find a way to smash themselves into one of the tethers. Thus, while it may take a while, installing these things would probably clear the low orbit space of all pre-existing objects, leaving clouds of extremely fast-moving, tiny, and lethal debris in their place (remember the film Gravity?). I need to research this point further, however.

Right. If your eyes haven’t glazed over yet, then you’re a good candidate for my geeky style of writing! And you should definitely read more from the authoritative sources: NASA’s Catalog of Earth Satellite Orbits for the easy overview, and then Terry Burlison’s Rendezvous and Docking: a User’s Guide for Non-Rocket Scientists for something deeper (he calls it “Part 1,” but I’ve never found a “Part 2,” sadly).

And if your eyes have glazed over, but you still managed to read this far, then you’re probably a great candidate to beta read my writing in order to rein me in a bit and get me to focus on the story and not all this technical stuff. ‘Cause obviously I can get myself way off-track with it all!

s127e012938
image credit: NASA

header image credit: user:SpaceX-Imagery / pixabay.com

WorkInProgress: Geostationary

On By Matt FraserIn Serial, Work in ProgressLeave a comment

This scene obviously took me a bit longer to finish than the others before it, as I wrestled with a number of factors. Not least among those was simply figuring out how the crew would go about forcing their way into an alien space station, one that has no direct analog to our technology or knowledge.

That turns out not to be that big of a deal in the end. Is there a hatch on the station? Well, yes, the aliens would have needed a way to get in and out. Ok, so how different can a hatch be? Well, it might be quite a bit smaller, for one thing, if the alien species is quite different in size from humans. But otherwise, it’s still going to be essentially a door, and a door must have some mechanism for opening it.

But… what if the aliens don’t have hands in the way that we do? What if they have claws, instead? Hmm, well, a handle for claws is probably not too different than a handle for hands, assuming those claws can grasp something. And if they can’t, then we don’t have much in the way of tool users in the early history of those aliens, do we?

Do we? Oh, we could go down so many interesting rabbit holes with this one. I think we’ll return to this subject in a later post.

Ok, so there’s a hatchway, possibly a bit of a tight fit, but still a hatchway, and it has a handle. One that’s either frozen with disuse, or locked. Either way, it’s going to need some modicum of force to get in. Applying force, or cutting your way in, in vacuum, in microgravity. What could go wrong?

A lot could go wrong.

The other factor that kept me up late at night doing math puzzles was figuring out what a good parking orbit for Aniara would be relative to the space station. I spent a good part of the last two weeks reading and reading about orbital mechanics and astrodynamics, and my head still spins from some of the math involved. At one point I had myself convinced that, like Zeno’s arrow reaching its target, it was impossible to truly rendezvous in orbit.

Except we do it all the time with the ISS here at Earth.

There’s another post to come on this subject. This one is really quite fascinating to the geek in me.

However, for purposes of this ongoing serial story, there is one factor about Aniara‘s orbit that the careful reader will discern as a departure from the previous scene. In Flip and Burn, you may recall, the Captain, David Benetton, asks our pilot, Anna Laukkonnen, to bring the ship to a parking orbit 100 kilometers north of the station, and to a matching altitude.

However in the scene you’re about to read, Anna does something different. She parks the ship 100 kilometers higher than the station, but directly over it.

Why the change? That, my friends, is going to be the primary subject of my forthcoming post on orbital mechanics. Suffice it to say that after several evenings of scratching about on Excel, I realized that the only way to maintain the same altitude but a different inclination and not smash into the station (twice per orbit, in fact) would be through a fairly constant use of thrusters. This would be an expensive thing to do, in terms of using up not-unlimited propellant, and a responsible pilot wouldn’t do it when a safer alternative that uses far less fuel (or none at all) is readily available.

The risks of pantsing a novel, indeed. That detail in the previous scene will have to change in the rewrite.

Right, so more to come on this subject. Meanwhile, you’re tired of me driveling on about these boring topics, and just want to read a good scene, right? Well, here you go!

 

Geostationary

image credit: NASA

The Inherent Risks of Pantsing a Novel

On By Matt FraserIn Work in Progress, Writing Process2 Comments

You know what I mean, of course. Writing a novel “by the seat of your pants.” No detailed planning, only a vague plot idea in advance, making each scene up as you write it.

Sounds like no way to write a novel, does it? The Project Manager in me cringes at the very idea. If I approached my day job in this manner, it wouldn’t be long before I’d be out on my ear.

Yet… it’s a lot of fun. The characters definitely have minds of their own, and as the words fly onto the page, they let the author know in no uncertain terms just where they want to go, what they want to do. Of course, all is not peaches and cream for the characters, they don’t always get their way, and indeed sometimes things go very badly for them. Otherwise, there wouldn’t be much of a story, would there?

Hint: things are about to get a lot more tense for one or two of my characters, but I won’t say any more just yet.

The arc of the story, however, remains rather foggy for the author. This is the nature of pantsing. We know roughly where we’re going, but it’s a bit like navigating a boat through heavy fog with no chart, only a compass and perhaps a handheld GPS. You know where you are, you know where you want to go, and you know which direction to point the boat. But you have no idea what’s between you and your destination. Large ships may loom up out of the mist, threatening to crush you at any moment. And that bell you hear ringing? What’s that? Oh! There it is! It’s the navigation buoy, the one you were aiming for, dead ahead and… hard to starboard! Quick, or we’ll smash into the thing!

Ah, but we found it, the nav buoy, in the end, didn’t we? Sure, we almost ran it down, but now we know exactly where we are.

Pantsing is a bit like that, and like that ocean-going tug looming out of the fog, there come inflection points in the story, where things can go one way, or they can go another, and the author must make a momentous decision before continuing.

When Takashi opens that station hatch — because of course he’ll figure out a way, right? — what will he and the others find? What alien relics have the Keplerians left behind? What will be revealed about Aniara and her crew’s own situation? Are they in even more trouble than they yet realize?

Make one decision, and I could be sealing the fate for not just this crew, but for any other stories I may wish to write in this same universe in future. If I’m not careful, I could “break” the universe, making it unsuitable for further adventures, and, well, I really don’t want to do that. I have other story ideas, at least one of which has been hinted at in the narrative already.

Make a different decision, and the future of interstellar civilization could be assured. Well, as assured as any civilization can be where the fastest way to get a message from one place to another is to get on a ship and go there — no ansible here.

And yet…

There’s an appeal to having this story go a certain way. It would be… interesting. And risky.

After all, breaking an entire universe is a pretty heavy risk.

Side note: that bit about navigating a boat through fog with only a handheld (non-charting) GPS and a compass, and nearly being run down by a tug, and then nearly running down a buoy…. yeah, that happened. Ask me about it some day.

image credit: l_schwarze / pixabay.com

Work in Progress: Flip and Burn

On By Matt FraserIn Serial, Work in Progress2 Comments

A two-fer!

I’ve combined two scenes into a single post here, mainly because one of them was quite a bit shorter than all the others so far (just under 500 words), and also because I felt like keeping on writing after that one.

You’ll recall that the crew of the starship Aniara has been accelerating in toward the planet Kepler 62f, around which they’ve discovered what appears to be an orbital ring station — the first indication that somebody once lived here, even if they may not be here any longer. They are now halfway there, and it’s time to begin decelerating.

The “flip and burn” maneuver. No, I didn’t coin that phrase. For that, I have to credit a pair of my favorite authors, collectively known as James S.A. Corey (a pen-name for the writing duo Daniel Abraham and Ty Franck), best known for their science fiction series The Expanse (and the SyFy TV series of the same name). In the opening chapters of the first book, and the pilot episode of the show, the interplanetary ice hauler Canterbury needs to alter their acceleration trajectory in order to respond to a distress call. The executive officer, James Holden, warns the crew, “This will be a high-G maneuver. Prepare for flip and burn.” (I think the dialogue in the book was slightly different from that in the show, but I digress.)

That, right there, was what made me want to see that show, and then after to read those books, which I now consume just as fast as Abraham and Franck can churn them out. No magic “artificial gravity,” no spaceships that fly around like fighter jets in an atmosphere, just full Newtonian physics at work. If you want to change the direction of your ship, or slow it down, you need to point engines ahead of your travel vector and burn.

If your engines are efficient enough, and you can carry enough propellant, then the fastest way to get somewhere is to accelerate constantly until you reach the halfway point, then flip the ship around and decelerate the rest of the way. That’s without taking into account matching aphelion and perihelion of initial and final orbits, but again, I digress.

Aniara, of course, is not burning as hard as the Canterbury. She’s moving very fast, due to twenty-one days of constant acceleration, but the acceleration itself is relatively minor. At the halfway point, the crew shuts down the engine, flips the ship, and restarts it, for twenty-one days of deceleration. They aren’t changing the direction of their vector, just reducing speed, so no massive G forces on superstructure or crew are necessary.

So, that’s our first scene here, followed by arrival at the ring station. Enjoy!

The Silence of Ancient Light: Flip and Burn

image credit: NASA

space asteroids planet

Working Titles

On By Matt FraserIn Writing ProcessLeave a comment

So if you’re a writer, do you ever find yourself stuck trying to find the perfect title for your forthcoming masterpiece before you ever set pen to paper (or fingers to keyboard, as it may be for most of us these days)? Most writing advice says “Don’t worry about it at this stage,” to pick a “working title” and work on your prose itself, then come up with the “real” title later.

But so many of the tools we use, whether it’s Scrivener or Word, Dramatica or Contour, or even WordPress, seem to encourage us to have that title before doing anything else. You need to save your work (early and often), and to do that you need a filename. If you later change the title, you could keep the same filename, but probably you’ll want to change that too. Not really a big deal, but there it is.

If you’re like me and publish your drafts online (you have been reading my work-in-progress, haven’t you?), naturally you need a title before you click that Publish button, but it goes beyond that. As soon as you publish anything to the web, it has a URL. Later, if you change the title, you’re faced with a very serious decision: do you change the URL?

Changing URLs has consequences. For one thing, once Google (or Bing or Yahoo) has indexed your site, there will be links to that old URL for search engines to find. If that URL ceases to function, now there’s a broken link, and yes, Google will punish you in search rank for having broken links. They don’t like that. And they don’t like it because readers don’t like it, either. Clicking a link to get the dreaded 404 error message tends to turn people away. And some readers, if you’re very lucky, may have even bookmarked that URL for later reading.

So, you could leave the URL alone, but just change the “friendly” name of the page, and then you end up with what I have here.

Because, friends, I am changing the working title of my work-in-progress. Previously known as Celestes, I knew this would never be the final title of the piece, as it didn’t even grab me all that strongly. Seeing the reactions of friends to the name only solidified me in the decision to change it, and to change it now.

So, I invite you to follow along with The Silence of Ancient Light as the story continues, and not to worry about the “slug” or URL for the four scenes already published as Celestes. And who knows? Maybe this title will survive to the end.

What do you think? Is this better? Not good enough? What are some of your favorite titles (whether or not they’re your favorite books), science fiction or otherwise?